Quantum Mechanics

"In the brief period between 1900 and 1935 there occurred one of the most astonishing outbursts of scientific creativity in all of history. ...no other historical era has crammed so much scientific creativity, so many discoveries of new ideas and techniques, into so few years. Although a few outstanding individuals dominate... they were assisted in their work by an army of talented scientists and technicians."

"In the years 1925 and 1926 modern quantum theory came into being fully fledged. These anni mirabiles remain an episode of great significance in the folk memory of the theoretical physics community... Werner Heisenberg had been struggling to understand the details of atomic spectra. ...Heisenberg's discovery came to be known as matrix mechanics. ...In 1925 matrices were... mathematically exotic to the average theoretical physicist... Prince Louis de Broglie... made the bold suggestion that if undulating light also showed particle-like properties... one should expect particles such as electrons to manifest wavelike properties... by generalizing the Planck formula. The latter had made the particlelike property of energy proportional to the wavelike property of frequency. De Broglie suggested that... particlelike... momentum... should analogously be related to... wavelength, with Planck's universal constant again... These equivalences provided... for translating from particles to waves, and vice versa. In 1924, de Broglie laid out these ideas in his doctoral thesis. ...To attain a full dynamical theory, a further generalization... allowed the incorporation of interactions... This is the problem that Schrödinger succeeded in solving. Early in 1926 he published the famous equation... led to its discovery by exploiting an analogy drawn from optics."

"The quantum revolution describes our deepest insight, so far, into the physical structure of nature. It is comparable only with the Copernican revolution, switching from a finally oriented anthropomorphic description of physical phenomena to one using general laws with initial or boundary conditions, connected with the names Kepler, Galileo, and Newton, or with the change from tangible mass points as basic structures to Faraday's and Maxwell's field concepts and, shortly before quantum theory, with the relativization of space and time by the lonely genius Einstein."

"Quantum mechanics, created early this century in response to certain experimental facts which were inexplicable according to previously held ideas (...'classical physics'), caused three great revolutions. In the first place it opened up a completely new set range of phenomena to which the methods of physics could be applied. ...The second revolution was the apparent breakdown of determinism, which had always been an unquestioned ingredient and an inescapable prediction of classical physics. ...The outcome of any particular experiment is not, even in principle, predictable, but is chosen at random from a set of possibilities; all that can be predicted is the probability of particular results when the experiment is repeated many times. ...even if we had complete knowledge of the initial state... The third revolution ...challenged the basic belief, implicit in all science and indeed in almost the whole of human thinking, that there exists an objective reality ...that does not depend for its existence on its being observed."

"Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution."

"Turning to quantum mechanics, we know immediately that here we get only the ability, apparently, to predict probabilities. Might I say immediately, so that you know where I really intend to go, that we always have had (secret, secret, close the doors!) we always have had a great deal of difficulty in understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it. And therefore, some of the younger students ... you know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. It has not yet become obvious to me that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem. So that's why I like to investigate things. Can I learn anything from asking this question about computers—about this may or may not be mystery as to what the world view of quantum mechanics is? So I know that quantum mechanics seem to involve probability—and I therefore want to talk about simulating probability."

"In less than ten years quantum computers will begin to outperform everyday computers, leading to breakthroughs in artificial intelligence, the discovery of new pharmaceuticals and beyond. The very fast computing power given by quantum computers has the potential to disrupt traditional businesses and challenge our cyber-security. Businesses need to be ready for a quantum future because it's coming."

"Back in the 1940s, researchers were just discovering how to use vacuum tubes as simple switches. … These switches could then form logic gates, which could be linked together to form the first logic circuits. That’s where we’re at now with quantum processors. We have verified that all the components work. The next step is to engineer the smallest, yet most interesting circuit possible."

"Quantum computation is … nothing less than a distinctly new way of harnessing nature … It will be the first technology that allows useful tasks to be performed in collaboration between parallel universes, and then sharing the results."

"We show that Shor's algorithm, the most complex quantum algorithm known to date, is realizable in a way where, yes, all you have to do is go in the lab, apply more technology, and you should be able to make a bigger quantum computer … It might still cost an enormous amount of money to build — you won’t be building a quantum computer and putting it on your desktop anytime soon — but now it’s much more an engineering effort, and not a basic physics question."

"The problem of measurement and the observer is the problem of where the measurement begins and ends, and where the observer begins and ends. Consider my spectacles, for example: if I take them off now, how far away must I put them before they are part of the object rather than part of the observer? There are problems like this all the way from the retina through the optic nerve to the brain and so on. I think, that—when you analyze this language that the physicists have fallen into, that physics is about the results of observations—you find that on analysis it evaporates, and nothing very clear is being said."

"... quantum mechanics, as it is enshrined in s, seems to require separate rules for how quantum objects behave when we’re not looking at them, and how they behave when they are being observed. When we’re not looking, they exist in “s” of different possibilities, such as being at any one of various locations in space. But when we look, they suddenly snap into just a single location, and that’s where we see them. We can’t predict exactly what that location will be; the best we can do is calculate the probability of different outcomes. The whole thing is preposterous. Why are observations special? What counts as an “observation,” anyway? When exactly does it happen? Does it need to be performed by a person? Is consciousness somehow involved in the basic rules of reality? Together these questions are known as the “measurement problem” of quantum theory."

"If the packet is to be reduced, the interaction must have produced knowledge in the brain of the observer. If the observer forgets the result of his observation, or loses his notebook, the packet is not reduced. We are again led to emphasize the fact that the wave function of a pure-state assemblage is merely a mathematical tool for computing from all previous observations what the relative probabilities are for different results when we make our next observation."

"Quantum computational approaches improve upon classical methods for a number of specialized tasks. The extent of quantum computing’s applicability is still being determined. It does not provide efficient solutions to all problems; neither does it provide a universal way of circumventing the slowing of Moore’s law. Strong limitations on the power of quantum computation are known; for many problems, it has been proven that quantum computation provides no significant advantage over classical computation. Grover’s algorithm, the other major algorithm of the mid- 1990s, provides a small speedup for unstructured search algorithms. But it is also known that this small speedup is the most that quantum algorithms can attain. Grover’s search algorithm applies to unstructured search. For other search problems, such as searching an ordered list, quantum computation provides no significant advantage over classical computation. Simulation of quantum systems is the other significant application of quantum computation known in the mid-1990s. Of interest in its own right, the simulation of increasingly larger quantum systems may provide a bootstrap that will ultimately lead to the building of a scalable quantum computer. After Grover’s algorithm, there was a hiatus of more than five years before a significantly new algorithm was discovered. During that time, other areas of quantum information processing, such as quantum error correction, advanced significantly. In the early 2000s, several new algorithms were discovered. Like Shor’s algorithm, these algorithms solve specific problems with narrow, if important, applications. Novel approaches to constructing quantum algorithms also developed. Investigations of quantum simulation from a quantum-information-processing point of view have led to improved classical techniques for simulating quantum systems, as well as novel quantum approaches. Similarly, the quantum-information-processing point of view has led to novel insights into classical computing, including new classical algorithms. Furthermore, alternatives to the standard circuit model of quantum computation have been developed that have led to new quantum algorithms, breakthroughs in building quantum computers, new approaches to robustness, and significant insights into the key elements of quantum computation."

"If collapse actually worked the way its adherents say it does, it would be:1. The only non-linear evolution in all of quantum mechanics. 2. The only non-unitary evolution in all of quantum mechanics. 3. The only non-differentiable (in fact, discontinuous) phenomenon in all of quantum mechanics. 4. The only phenomenon in all of quantum mechanics that is non-local in the configuration space. 5. The only phenomenon in all of physics that violates CPT symmetry. 6. The only phenomenon in all of physics that violates Liouville's Theorem (has a many-to-one mapping from initial conditions to outcomes). 7. The only phenomenon in all of physics that is acausal / non-deterministic / inherently random. 8. The only phenomenon in all of physics that is non-local in spacetime and propagates an influence faster than light.WHAT DOES THE GOD-DAMNED COLLAPSE POSTULATE HAVE TO DO FOR PHYSICISTS TO REJECT IT? KILL A GOD-DAMNED PUPPY?"

"To Einstein the collapse postulate was an even more pernicious retreat from realism than that described above: it implied that physical quantities usually have no values until they are observed, and therefore that the observer must be intrinsically involved in the physics being observed. This suggests that there might be no real world in the absence of an observer!"

"Unfortunately, people writing about quantum mechanics often use the phrase "collapse of the wave-function" to describe what happens when an object is observed. This phrase gives a misleading idea that the wave-function itself is a physical object. A physical object can collapse when it bumps into an obstacle. But a wave-function cannot be a physical object. A wave-function is a description of a probability, and a probability is a statement of ignorance. Ignorance is not a physical object, and neither is a wave-function. When new knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant."

"Bohr’s principle of complementarity – the heart of the Copenhagen philosophy – implies that quantum phenomena can only be described by pairs of partial, mutually exclusive, or ‘complementary’ perspectives. Though simultaneously inapplicable, both perspectives are necessary for the exhaustive description of phenomena. Bohr aspired to generalize complementarity into all fields of knowledge, maintaining that new epistemological insights are obtained by adjoining contrary, seemingly incompatible, viewpoints. [...] The value of Bohr’s philosophy for the advancement of physics is controversial. His followers consider complementarity a profound insight into the nature of the quantum realm. Others consider complementarity an illuminating but superfluous addendum to quantum theory. More severe is the opinion that Bohr’s philosophy is an obscure ‘web of words’ and mute on crucial foundational issues."

"In contemplating the papers Einstein wrote in 1905, I often find myself wondering which of them is the most beautiful. It is a little like asking which of Beethoven’s symphonies is the most beautiful. My favorite, after years of studying them, is Einstein’s paper on the blackbody radiation. [...] Part of being a great scientist is to know—have an instinct for—the questions not to ask. Einstein did not try to derive the Wien law. He simply accepted it as an empirical fact and asked what it meant. By a virtuoso bit of reasoning involving statistical mechanics (of which he was a master, having independently invented the subject over a three-year period beginning in 1902), he was able to show that the statistical mechanics of the radiation in the cavity was mathematically the same as that of a dilute gas of particles. As far as Einstein was concerned, this meant that this radiation was a dilute gas of particles—light quanta. But, and this was also characteristic, he took the argument a step further. He realized that if the energetic light quanta were to bombard, say, a metal surface, they would give up their energies in lump sums and thereby liberate electrons from the surface in a predictable way, something that is called the photoelectric effect. [...] In the first place, not many physicists were even interested in the subject of blackbody radiation for at least another decade. Kuhn has done a study that shows that until 1914 less than twenty authors a year published papers on the subject; in most years there were less than ten. Planck, who was interested, decided that Einstein’s paper was simply wrong."

"The two photons are entangled and according to local realism, their polarization planes should become independent... a typical EPR situation. Already in 1948, observations... agreed with quantum mechanics, not with local realism."

"There is a troubling weirdness about quantum mechanics. Perhaps its weirdest feature is entanglement, the need to describe even systems that extend over macroscopic distances in ways that are inconsistent with classical ideas."

"The phenomenon of entanglement is the essential fact of quantum mechanics, the fact that makes it so different from classical physics. It brings into question our entire understanding about what is real in the physical world. Our ordinary intuition about physical systems is that if we know everything about a system, that is, everything that can in principle be known, then we know everything about its parts. If we have complete knowledge of the condition of an automobile, then we know everything about its wheels, its engine, its transmission, right down to the screws that hold the upholstery in place. It would not make sense for a mechanic to say, “I know everything about your car but unfortunately I can’t tell you anything about any of its parts.” But that’s exactly what Einstein explained to Bohr — in quantum mechanics, one can know everything about a system and nothing about its individual parts — but Bohr failed to appreciate this fact. I might add that generations of quantum textbooks blithely ignored it."

"When two systems, of which we know the states by their respective representation, enter into a temporary physical interaction due to known forces between them and when after a time of mutual influence the systems separate again, then they can no longer be described as before, viz., by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics."

"He [Albert Einstein] didn’t think the spooky action at a distance would be verified, but it was, He thought that was somehow unphysical. He presented this as an example of why quantum mechanics is probably wrong, but in fact it’s right."

"... you consider my attitude towards to be strange and archaic. ... the theory cannot be reconciled with the idea that physics should represent a reality in time and space free from spooky actions at a distance."

"I'd like to think that the moon still exists, even if I'm not looking at it."

"Quantum theory is now discussing instantaneous connections between two entangled quantum objects such as electrons. This phenomenon has been observed in laboratory experiments and scientists believe they have proven it takes place. They’re not talking about faster than the speed of light. Speed has nothing to do with it. The entangled objects somehow communicate instantaneously at a distance. If that is true, distance has no meaning. Light-years have no meaning. Space has no meaning. In a sense, the entangled objects are not even communicating. They are the same thing. At the “quantum level” (and I don’t know what that means), everything may be actually or theoretically linked. All is one. Sun, moon, stars, rain, you, me, everything. All one."

"When the quantum system contains more than one particle, the superposition principle gives rise to the phenomenon of entanglement. It is now not just a particle interfering with itself—it is a system interfering with itself: an entangled system. Amazingly enough, Erwin Schrödinger himself realized that particles or photons produced in a process that links them together will be entangled, and he actually coined the term entanglement, both in his native German and in English. Schrödinger discovered the possibility of entanglement in 1926, when he did his pioneering work on the new quantum mechanics, but he first used the term entanglement in 1935, in his discussion of the Einstein, Podolsky, and Rosen (EPR) paper."

"The discomfort that I feel is associated with the fact that the observed perfect quantum correlations seem to demand something like the ‘genetic’ hypothesis [identical twins, carrying with them identical genes]. For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave. This is so rational that I think that when Einstein saw that, and the others refused to see it, he was the rational man. The other people, although history has justified them, were burying their heads in the sand. I feel that Einstein’s intellectual superiority over Bohr, in this instance, was enormous; a vast gulf between the man who saw clearly what was needed, and the obscurantist. So for me, it is a pity that Einstein’s idea doesn’t work. The reasonable thing just doesn’t work."

"Einstein’s great friend and intellectual sparring partner Niels Bohr had a nuanced view of truth. Whereas according to Bohr, the opposite of a simple truth is a falsehood, the opposite of a deep truth is another deep truth. In that spirit, let us introduce the concept of a deep falsehood, whose opposite is likewise a deep falsehood. It seems fitting to conclude this essay with an epigram that, paired with the one we started with, gives a nice example:“Naïveté is doing the same thing over and over, and always expecting the same result.”"

"In the famous Einstein–Bohr debates, Bohr defended quantum mechanics against Einstein's yearning for a more classical theory; but some of us are coming to feel in defending his hard-won ground he compromised too much. Quantum mechanics should be pushed as hard as possible, to the point where it can describe within itself a recognizable caricature of the world as it is experienced, and thus begin to provide its own self-consisted interpretation — or else there should be some definite change in its equations. As yet this task has not been accomplished."

"The other mistake that is widely attributed to Einstein is that he was on the wrong side in his famous debate with Niels Bohr over quantum mechanics, starting at the Solvay Congress of 1927 and continuing into the 1930s. In brief, Bohr had presided over the formulation of a “Copenhagen interpretation” of quantum mechanics, in which it is only possible to calculate the probabilities of the various possible outcomes of experiments. Einstein rejected the notion that the laws of physics could deal with probabilities, famously decreeing that God does not play dice with the cosmos. But history gave its verdict against Einstein—quantum mechanics went on from success to success, leaving Einstein on the sidelines. All this familiar story is true, but it leaves out an irony. Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe."

"To this day, many researchers agree with Bohr's pragmatic attitude. The history books say that Bohr has proved Einstein wrong. But others, including myself, suspect that, in the long run, the Einsteinian view might return: that there is something missing in the Copenhagen interpretation. Einstein's original objections could be overturned, but problems still arise if one tries to formulate the quantum mechanics of the entire universe (where measurements can never be repeated), and if one tries to reconcile the laws of quantum mechanics with those of gravitation. But I am running far ahead in my story (I will return to this point in chapter 28). For a correct description of atoms and molecules, quantum mechanics is a perfect theory."

"Albert Einstein, who was in many ways the father of quantum mechanics, had a notorious love-hate relation with the subject. His debates with Niels Bohr—Bohr completely accepting of quantum mechanics and Einstein deeply skeptical— are famous in the history of science. It was generally accepted by most physicists that Bohr won and Einstein lost. My own feeling, I think shared by a growing number of physicists, is that this attitude does not do justice to Einstein’s views. Both Bohr and Einstein were subtle men. Einstein tried very hard to show that quantum mechanics was inconsistent; Bohr, however, was always able to counter his arguments. But in his final attack Einstein pointed to something so deep, so counterintuitive, so troubling, and yet so exciting, that at the beginning of the twenty-first century it has returned to fascinate theoretical physicists. Bohr’s only answer to Einstein’s last great discovery—the discovery of entanglement—was to ignore it."

"The refutation of Einstein’s criticism does not add any new element to the conception of complementarity, but it is of great importance in laying bare a very deep-lying opposition between Bohr’s general philosophical attitude and the still widespread habits of thought belonging to a glorious but irrevocably bygone age in the evolution of science."

"We, of course, were sure that on that particular debate Bohr was right and Einstein was wrong."

"The famous debate between Einstein and Bohr began at the Solvay Council in 1927. The debate was about the interpretation of quantum mechanics, but also addressed the fundamental question of what the purpose and aim of a physical theory should be. Their conflicting positions were based on two diametrically opposed philosophical approaches to the fundamental problems of physics. The many books popularising quantum mechanics quite rightly place the emphasis on the problem of interpretation: they discuss the opposing positions of Einstein’s “realism” and the “Copenhagen interpretation” of which Bohr is seen as the leading protagonist."

"Einstein's thinking is always on the ontological level traditional in physics; trying to describe the realities of Nature. Bohr's thinking is always on the epistemological level, describing not reality but only our information about reality."

"Their dispute went to the fundamental heart of the design of the cosmos. Was there an objective reality that existed whether or not we could ever observe it? Were there laws that restored strict causality to phenomena that seemed inherently random? Was everything in the universe predetermined?"

"Einstein was not prepared to let us do what, to him, amounted to pulling the ground from under his feet. Later in life, also, when quantum theory had long since become an integral part of modern physics, Einstein was unable to change his attitude—at best, he was prepared to accept the existence of quantum theory as a temporary expedient. "God does not throw dice" was his unshakable principle, one that he would not allow anybody to challenge. To which Bohr could only counter with: "Nor is it our business to prescribe to God how He should run the world.""

"The mid-twentieth century “Bohr-Einstein debate” about quantum theory is often misinterpreted as a personal clash between wizards. So counter-intuitive are quantum theory’s predictions that, under the leadership of one of its pioneers, Neils Bohr, a myth grew that there is no underlying reality that explains them. Particles get from A to B without passing through the intervening space, where they have insufficient energy to exist; they briefly “borrow” the energy, because we are “uncertain” about what their energy is. Information gets from A to B without anything passing in between – what Einstein called “spooky action at a distance.” And so on....So, while most accounts say that Bohr won the debate, my view is that Einstein, as usual, was seeking an explanation of reality, while his rivals were advocating nonsense. Everett’s interpretation doesn’t make Einstein a demigod. But it does make him right."

"His thought experiment with photon and film had not challenged Heisenberg's principle, but now Einstein did turn his attention there. He began looking for an experiment that would allow a more complete collection of data than the Heisenberg team thought possible. If he could find a technique that allowed the simultaneous discovery of position and momentum or time and energy, he would prove the quantum mechanics had indeed not yet brought us to the the secret of the Old One. This effort led the most famous set-pieces of the Einstein "debate" with Bohr over quantum mechanics. Einstein, Bohr, and Ehrenfest would meet in the hotel dining room for breakfast. Einstein would propose a thought experiment. Bohr would think about it. ... During the day's program at Solvay, Heisenberg and Pauli would analyze the experiment that Einstein had proposed. They would find some point where the uncertainty principle fought back, and over dinner, Bohr wold refute the experimental effort while Ehrenfest looked on."

"The EPR paper came out in 1935 and for at least two decades no one paid much attention to it. However, in 1964, the late John Bell published a paper that changed everything. He showed that Einstein’s idea that the results of quantum mechanics could be reproduced by a theory in which Einstein’s notions of realism were included could be tested in the laboratory. Having spent a good deal of time talking to Bell I can tell you that his heart was with Einstein. He often referred to Bohr as an “obscurantist.” But the experiments were carried out by Alain Aspect and others and showed that Einstein was wrong and Bohr was right. I cannot believe that anyone familiar with this would still agree with Einstein."

"Bohr was inconsistent, unclear, willfully obscure and right. Einstein was consistent, clear, down-to-earth and wrong."

"To recap, I had four numbers to add together. If the total came to under 2, then Einstein’s version of quantum reality was correct and the world is deterministic, rather than probabilistic, with quantum entities existing prior to being observed. But if the total came to over 2, then Niels Bohr was right and there is no objective reality out there in the absence of measurement and the subatomic world is ruled by chance and probability. [...] So, sorry Einstein, victory goes to Bohr instead."

"At the first of the 1960's Rochester Coherence Conferences, I suggested that a license be required for use of the word photon, and offered to give such license to properly qualified people."

"Une hypothèse qui permet de prévoir certains effets qui se reproduisent toujours ressemble absolument à une vérité démontrée. Le système de Newton ne repose guère sur un autre fondement. Si en réalité et de l aveu du. [A hypothesis which permits the prediction of certain effects that always reoccur under certain conditions does, in its way amount to a demonstrable certainty. Even the Newtonian system had no more than such a foundation.]"

"... Heisenberg's main work — his wonderful work — on the uncertainty principle ... Some very important people — like Einstein — did not like this. ... His remark was, "I can believe that God governs the world with any set of laws, but I cannot believe that He is playing at dice. ..." ... Einstein's statement — his remark — was really something to the effect: "I cannot imagine any science without causality ...""

"Werner Heisenberg not only discovered but proved that in certain subatomic situations neither classical objectivity nor mechanical causality applied: that the act of the physicists observation (more exactly: his attempts at measurement) interfered either with the movement or with the situation of the object—which meant, among other things, a big crack in the fundament of Descartes's and Newton's objectivism and determinism. In other words: the study of the "reality" of matter was inseparable from the interference (and from the mind and purpose) of the scientist."

"Heisenberg considered the observation through a microscope of an electron struck by light of an appropriate frequency. The position of the electron could be determined more precisely by increasing the frequency of the light, but the higher the frequency, the larger the jolt to the electron, and, hence, the greater the indeterminacy in the measurement of the electron's velocity. Conversely, the velocity could be determined more precisely by using light of a lower frequency, but the lower the frequency, the greater the indeterminacy in the measurement of the position. On the basis of these considerations, Heisenbery boldly affirmed the acausality of quantum mechanics: For to predict the future, you had to know everything about the present, and according to quantum mechanics, Heisenberg asserted, "We cannot, as a matter of principle, know the present in all its details.""